You can search far an wideYou can drink the whole town dryBut you'll never find a beer so brownAs the one we drink in our home townYou can drink your fancy alesYou can drink 'em by the flagonBut the only brew for the brave and trueComes from the Green Dragon

Too bad they only name the "Dragon Knights". The other faction seems only to be referred to as "the knights" or "the king's army" or other similarly unhelpful things. I think I might go with "Red Lions", personally.